Small changes can have a big impact. But can a butterfly’s wing-beat in the Amazon really impact the weather halfway across the world? And where do small changes have no impact?
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Fraser Cain: Astronomy Cast Episode 435: The Butterfly Effect
Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos, where we help you understand not only what we know but how we know what we know.
My name is Fraser Cain. I’m the publisher of Universe Today and with me is Dr. Pamela Gay, the director of CosmoQuest.
Hey, Pamela. How are you doin’?
Dr. Pamela Gay: I’m doin’ well, Fraser. How are you doing?
Fraser Cain: Great.
Tell us how they can donate.
Dr. Pamela Gay: So, some of our avid listeners noticed that we stopped having a donation link for a little while and we weren’t mentioning it at the end of the show. Well, that’s because we’ve been in the process of migrating Astronomy Cast from Southern Illinois University via Astrosphere New Media, which was a stopgap measure, over to the Astronomical Society of the Pacific, which is going to be the new home institution for CosmoQuest, for Astronomy Cast, for a whole lot of really good things and you’re going to be hearing more and more about that in the coming weeks.
But for now, please go over and donate so that we can pay Chad and pay Susie and all that sort of stuff because, since we didn’t ask for donations for several months, we’re kind of poor right now.
Fraser Cain: Please do.
Dr. Pamela Gay: Yes.
Fraser Cain: And I think that will – What you just said, and we’ll give more information, will validate a whole bunch of people’s conspiracy theories. So, let’s –
So, small changes can have a big impact. Can a butterfly’s wing beat in the Amazon really impact the weather halfway across the world? And where do small changes have no impact?
Okay, this is a Pamela topic but, of course, I’m totally, totally on board. So why don’t you give people sort of an explanation or a description of the butterfly effect if anyone has never heard of it before.
Dr. Pamela Gay: So, the butterfly effect is this idea that if a butterfly flaps its wings in New Mexico, a typhoon will form off the coast of China. And that the entire reason that that typhoon ends up forming is because of the impact that that simple difference had on the atmosphere and that hurricane, typhoon, would never, ever have occurred without that minute, tiny change to the starting parameters of that moment in time.
Fraser Cain: Now, this is part of this idea of chaos theory and we’re not going to go into the whole concept of chaos theory for two reasons: 1) It’s not your specialty; and, 2) It’s a bottomless rabbit hole – and some really great books.
But – and I’m going to go on a complete side tangent here for a second, which was – Do you remember, there was, like, a book – or maybe it was a short story. Was it an Arthur C. Clarke, Robert Heinlein? I forget. Some kind of time travel device and they went back in time to, like, the dinosaur age and they stepped on a butterfly and everything was different. And they came back and then they noticed that there was – they were going to, like – hunting dinosaurs or something like that, back in the Jurassic Period, and then they got back and then they looked at the bottom of their shoe and there was a dead butterfly.
And so, that is the – So, just that one change of – I guess of stepping on a butterfly back in the Jurassic Period completely changed time in the future. But –
Dr. Pamela Gay: And one of the reasons that I picked this change is, we’re at a huge point in change – it feels like – for the whole planet. We’re watching the weather change. We’re watching politics change; there’s Trump, there’s Brexit. Everything is in flux. And I keep hearing random statements like: Well, so-and-so wouldn’t have happened if only I’d eaten something different for breakfast and you can’t prove me wrong.
Fraser Cain: Right, okay.
But, you know – strictly speaking – you know, where does the butterfly effect get, you know – Where do scientists sort of really consider this?
Dr. Pamela Gay: So, the reality behind the butterfly effect is: There are certain calculations – which means there are certain physical situations – where the smallest change in the initial parameters causes a radical difference later on. This whole concept actually came out of how many decimal places someone typed into a computer.
There was a meteorologist working at MIT, Edward Lorenz. And back in 1961, while he was working on a big, old, slow computer – fast for its day, best for its day, big, old, slow computer – he needed to rerun one of his atmospheric models and he didn’t want to rerun the entire simulation because that takes time, lots of it, because – 1961.
So, what he did was he picked it up partway through the run, typed in the number that was in his output – which was only output to three digits – and set the model going. And very, very quickly – just a couple months into the simulated time of his simulated weather pattern – the two graphs he was looking at were radically different; the models diverged greatly.
And he was trying to figure out – Had he, like, blown a vacuum tube? And I just love the idea that you’d get a different calculated value if you had vacuum tube failure. But it turns out what actually was happening was his software, when it went from one step in the model to the next, was using six digits. And the difference between the six-digit number he didn’t type in and the three-significant-digit number he did type in was enough to create wildly different scenarios for our atmosphere.
Fraser Cain: How many digits does reality have?
Dr. Pamela Gay: And that would be where the problem is.
Fraser Cain: Right.
Dr. Pamela Gay: So you have situations where it isn’t even possible to begin to understand all the different things that are going to have a massive impact on an outcome. And at the same time, which is the reason I wanted to bring this up, there are times where massive changes have absolutely no effect at all.
Fraser Cain: Right. And that was sort of the counter to this.
So, can – You know, there’s this idea that, you know, for certain kinds of situations, things will tend back towards the norm; that there is a damping effect that’s going on – that even if there are these changes, they have no impact. So can you give some examples of that?
Dr. Pamela Gay: So, for instance, if we tried to start the moon rotating again – just to throw out a crazy thing because this is what we do on Astronomy Cast. So, if you tried to start the moon rotating again, then it would eventually go back to exactly where it is right now.
If you tried to de-sync the Galilean moons that are tidally locked – not tidally locked, that have synchronized orbits – they would eventually work themselves back to exactly where they are right now.
So we have these situations where you try to change the outcome – and we’ve all experienced this with human interactions. Some of us have tried to do crazy things like: I had my Jeep emergency brake not work real well once and I attempted to stop my rolling Jeep with my own force of effort and it didn’t work quite as well as the curb it hit two feet later. Nothing was injured in the rolling of Pamela’s Jeep.
Fraser Cain: I think somebody died recently from their Jeep rolling back – from the cast of Star Trek.
Dr. Pamela Gay: Yeah, we’re not going to go that far.
Fraser Cain: Yeah, yeah.
Dr. Pamela Gay: No, I was careful not to get myself trapped anywhere.
Fraser Cain: Okay, good.
Dr. Pamela Gay: Yeah.
But there are situations where radical change does not change the outcome of the scenario and there are times when radical change in the outcomes comes from the smallest change in the input. And this is where, when we’re trying to understand various scientific ideas – if we’re trying to model, for instance, the origins of our solar system – we need to run the model in a variety of different ways.
So this is where we talk about Monte Carlo simulations. Because if there’s a simulation where there’s no preferred outcome, we have no way of figuring out what is going to happen. And if there is a model where only one of a million different scenarios gets to our particular solar system, it means that we may not be able to cleanly say, “This is how we got here,” because maybe there’s another scenario that also has one outcome that gets us to where we are right now.
Fraser Cain: Well, I think there’s a couple of examples where this has worked out quite significantly. And I think one is talking about orbital predictions. Right? You’re looking at the future of orbital – trying to figure out the future of where these objects are going to be.
And a great example of this is, for example, the, you know, close fly-bys of asteroids; potential impacts of asteroids, far in the future. There are a ton of tiny influences to these asteroids: There’s the influence of the gravity of Jupiter; there’s the paths of the Earth and the Mars; and then the shape of the object. And over time, the noise gets bigger than the prediction and so then, it’s literally the future of this object is in a fog. You just don’t know.
Dr. Pamela Gay: And what’s amazing with situations like this is, it is so complex and so easily changed that – with the specific example of asteroids, where at the drop of white paint long-term, has a massive change because it changes the reflectivity of the object. All of these changes add up over time. And because there are so many different things: The outgassing of volatiles trapped inside the asteroid; the differences in exactly the angle at which it’s rotating, which will cause differences in where it gets illuminated. Slight changes in all of these things cause the forces that are imparted on it – from solar radiation, from change in momentum, from light bouncing off of it; all of these things – to, well, change its orbit.
Fraser Cain: And so, I think, you know, if you’re a researcher who’s observing asteroids and it’s your job to predict whether or not the Earth is going to be safe from an asteroid impact any time in the future and whether we need to send a bunch of plucky, deep-oil drillers to the asteroid to – I don’t know, whatever they do Bruce Willis said.
What, you know – Where will your models fall apart? What is the – sort of the limits and how do scientists deal with the limits of what they can predict and what just enters into uncertainty-realm because of this butterfly effect?
Dr. Pamela Gay: It really depends on how rapidly the system is evolving.
So, for instance, a completely rocky asteroid, metal asteroid – something that is not outgassing – we can predict that if it has no close encounters with large objects like Earth, we can predict that for a long period of time; thousands, tens of thousands of years, depending on just how isolated it is. But something like a comet, which has all sorts of outgassing going on – all sorts of unknowns hidden deep in the coma – it gets a lot harder to predict.
This is what makes the reading of the book, Lucifer’s Hammer, which has a lot of issues but the science is good. It’s ignoring the issues. The science in it is based on this whole “we don’t know what happens when a comet passes close to the sun” because it could fall apart; it could keep going. We don’t know what crust is in there. And each of these things can have its own effect and all of these things can, well, snowball together to either cause life or cause death.
Fraser Cain: And I think one of the other big examples – I mean, that’s my favorite example, is just the difficulty of predicting forward.
But the other one is looking back and trying to understand the way the universe – the evolution at the largest scale of the universe over time – how we got to where we are right now. And this is this idea that astronomers, cosmologists go back, look at sort of the basic constituents – what was in place in the early universe – and then try to understand and replicate the structures that we see today. And, same thing – tiny little changes make dramatic impact on the nature of the universe that is simulated.
Dr. Pamela Gay: And what gets me is how much this factors into things as fundamental as: How the heck did our moon get there? Because it could have been depending on the angular momentum of the incoming system. It could have been all of these small changes, in this case, all lead to the same result: A moon. So you can have all sorts of different catastrophes that are radically different lead to the same outcome.
Fraser Cain: And this is another kind of rabbit hole, but this idea – this sort of – the idea of future civilizations running ancestor simulations. Right? That they’re going to go and run the history of the universe again and again and again and again to try and get a version of the universe that kind of matches the one that we find ourselves in today.
And we’re taking our first, really basic examples of it but there’s some pretty great simulations of the universe now that have replicated the large-scale structure of the universe to a level of accuracy that you really can then turn around and go all the way back to the beginning of, you know, the earliest stages of the universe and match it – you know, match it all up.
So I think one of the other really big ones that we’re dealing with is climate change. Right? Of the changing weather patterns in the Earth. And again, we, you know – we don’t know all the factors and so it’s super-hard to predict the future except it’s going to get weird.
Dr. Pamela Gay: And the way that I look at a lot of climate change things is, at a certain point, you have nice, friendly oscillations in the weather cycle, globally. And, at a certain point, the string on your pendulum breaks and things go flying off. Or another way to think of it is, things are pretty steady state, up until the point when you tip the system such that your state slides down.
And we’ve all been there, trying to stack things in the kitchen sink until, all of a sudden, nope – gonna crash. Or we’ve set things on – The one I do that drives people crazy is I’ll set my laptop on a sloped beanbag knowing friction will hold it in place, until the dog comes along and changes the slope just enough that it starts sliding. And because of the vagaries of humidity, of how dirty is my laptop, of how roughed up is that part of the beanbag, the angle at which it starts radically sliding is going to vary from day to day.
And with climate change, we honestly don’t know if we’re past the point of no return for our planet or not.
Fraser Cain: Yes, right. And I think we also sort of don’t know which of the factors that have been predicted – like, you know, we think about things like the Gulf Stream changing its course, which causes changes in levels – ice levels – in the Arctic. Or release of methane, you know, in these huge trapped stores. Is that going to have some impact? Will these things start to cause an acceleration?
I can think of one more analogy, which I think is sort of similar, is this – You know, we talked about the Lagrange points and we did a whole episode about these, right? But you’ve got these – sort of these two classes of Lagrange points. You’ve got the ones that are stable; they are like the bottom of a valley and if you’d roll a boulder into it, it’s going to sort of go back and forth and end up at the bottom of the valley. And you’ve got the ones that are unstable; where they’re sitting at the very top of a mountaintop and if you give it just a little bit of a push, it’s going to roll down and move out. And so you’ve got some objects that you can place in some of the – you know, the three Lagrange points that are lined up with the two bodies – and then the two that are perpendicular, those are stable.
And you’ve got just these two situations and you kind of almost don’t even – You know, in some situations, with some of this science, you don’t know which one of these cases you’re in. Are you in the one where the small changes revert back to the norm or are you in the one where the small changes will accelerate and sort of compile with each other into territory that was never predicted by your models?
Dr. Pamela Gay: And one of the things that’s important to remember is, there is a difference between being at an inflection point and the butterfly effect. So, for instance, it could be that you’re at a point where a miniscule change to the left – no change at all; whole outcomes are going to be absolutely unchanged. Small step to the right – massive change.
So, to use a completely exaggerated, interesting-to-middle-schoolers example, we know that the temperature of the Pacific Ocean has deep impact on weather patterns and huge effects on the rain in California and in Africa. Well, if you dumped a glass of cold water that you’re drinking into the ocean while you’re out swimming off of a – I don’t know – fishing boat, everything might be totally fine. Whereas, if you instead pee in the ocean, you put it over the edge and suddenly you’ve hit the trigger point.
Now, this is an exaggeration meant to amuse the middle-school brains in all of us but that’s an inflection point versus it being the butterfly effect, where two miniscule changes in any direction have radical changes in the output.
Fraser Cain: So, as a researcher, and as you’re, you know, putting together your work and trying to make models and predictions of the future – which is something that we always want, right? I mean, this – A part of it is that we, as human beings, want some certainty about the future. We want to know what is going to happen down the road and what is, you know – which of the ones. Should I floss my teeth? Should I recycle my garbage? Should I –
You know, these are all things that we, as human beings, want to know and the onus is on the science researchers to make these kinds of predictions.
So, what are the – you know, if you are a researcher or if you’re trying to look at research from afar that’s making some kind of prediction – how do you know it’s into this kind of territory and how can you kind of minimize the uncertainty and impact of what you’re doing?
Dr. Pamela Gay: The question you have to always ask is: What is the dominant variable?
So, to use examples like you were talking about, we’re now finding that the relative variable for whether or not you get cavities is not necessarily flossing your teeth, it is not necessarily how much candy you eat, but in many cases, it has to do with what flora, what microbes and bugs you’ve picked up that are living in your mouth; that that floss and that everything else just probably isn’t going to affect. It’s going to happily sit there and chew on your teeth. So it might come down to: Who did you kiss when you were 12 behind the school gymnasium and you picked up the wrong flora from them?
There’ve been studies that have looked at relationships between: Did your mother have cavities and did you breastfeed and, thus, pick up some of that stuff?
So we have to try and figure out what are the dominant variables. And often, we misidentify the variables initially. So, thus, the decades of: And you must brush your teeth and floss two to three times a day, preferably three times. And I don’t know anyone who flosses at work unless they’ve really been yelled at by a dentist.
So we have to figure it out and we have to know that sometimes we’re going to be wrong. And it’s by: Okay, let me try moving this variable around and see. Oh! That’s where the impact is. Let me move this variable around. Oh, wait. No, that one has a bigger impact.
We have to check each of the variables, move them all around. And if it turns out there is one variable that causes things to go “utter chaos” when you change it the slightest amount, that probably tells you you can’t actually predict anything.
Fraser Cain: And I think a great example of seeing the butterfly effect play out is some of the crazy, real-time trading – computer software algorithms that were created, where these kind of crazy networks of computers were trading according to these models that the various financial people had developed – and they went off the rails. Various feedback mechanisms grew bigger and bigger and bigger, outside of what was expected. You got all these black – You know, you got black swan events and –
But these computers are designed to just make, you know – act on the information as quickly as the data and computers will allow them and you just get this enormous, cascading, feedback effect that just goes on and on and on. And that’s a good example, I guess, of your – of you not anticipating the implications of the model that you’ve created. It just gets bigger and bigger and bigger. And real money is at play and billions of dollars are lost until somebody comes in and flicks the switch.
Some things, there are no switches that you can flick, right?
Dr. Pamela Gay: And what’s crazy is, with the stock market example – There’s an amazing radio lab on this, actually. The length of the cable between the stock market and the trading computers actually has an effect with modern computers, because they’re so fast that the speed-of-light delays between the computer and implementing the trade matters. And so, they actually have a room set up so that all of the computers have the exact same electronic distance from the trades.
Fraser Cain: That’s crazy. Man.
So, you know, if there was like one kind of science that is sort of most greatly impacted by this – I mean, I think we talked about astronomy and we talked about sort of predicting orbits as one of the toughest ones in your field. What are some other places where people should be looking out for this?
Dr. Pamela Gay: It’s really anywhere that turbulence has to come in. Turbulence is the great evil.
So this is where, for instance, if you have a single hair on a otherwise completely smooth surface, that will change the airflow across that surface that will introduce turbulence into the airflow and radically change where a couple of the atoms in that airflow end up. And then that trickles down and those things hit other things and you have collisions and – that’s a small situation that may not actually have much of an impact beyond a closed room but turbulence, in general, it changes – it literally changes – the flow. And those changes add up quickly.
And if you’ve ever looked at turbulent water, for instance, coming out of an open fire hose, you can’t predict readily, from one instant to another, exactly where the splash is going to be; where the next droplet of water is going to fly off. And it’s that turbulence – that flap of the butterfly’s wing – that sends the air molecules, the water molecules, the flowing molecules – whatever they are – into a slightly different direction, that creates so many headaches.
Fraser Cain: So many headaches.
Well, thanks Pamela.
Oh – and I just want to let people know, if you’re watching this live on YouTube or if you want to watch the YouTube channel, we now spend half an hour answering people’s questions. So if you’re listening to this as a podcast and you want to see 30 minutes of more show, go ahead and check out the YouTube version of this episode. We’ll talk to you –
Dr. Pamela Gay: And remember: If your dog leaves a dog toy in the backyard, the air flowing across it will be different and you have just changed the world.
Fraser Cain: Nice. We’ll see you next week.
Dr. Pamela Gay: See ya.
Male Speaker: Thank you for listening to Astronomy Cast, a non-profit resource provided by Astrosphere New Media Association, Fraser Cain and Dr. Pamela Gay. You can find show notes and transcripts for every episode at astronomycast.com. You can email us at firstname.lastname@example.org. Tweet us @astronomycast. Like us on Facebook or circle us on Google Plus.
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Duration: 29 minutes